Precision analog electronic components such as logarithmic amplifiers (log amps) are used in a variety of applications. One such application is in optical scanners, which are devices that read incident light patterns to generate electrical signals that vary in accordance with the light patterns' brightness. Each electrical signal can then be converted into a series of digital bits which is readable by a computer. The Universal Product Code (UPC) scanner used in a supermarket checkout line is a simple type of scanner familiar to most people.
More sophisticated scanners can generate computer-readable representations of complex images, such as a document or photograph. A computer is then used to edit the image representation, combine it with other images or data such as text, and perform other operations such as image enhancement. With such a system, printing of the computer-readable image can be postponed until it is in the desired form. New applications for this process appear almost daily and it is only a matter of time before nearly every computer user will routinely use scanners in the preparation of reports, memoranda, and other business documents.
To create the computer-readable image representation, a scanner uses a light source and a photodetector. The light source is focused on a particular point, or pixel, of the image, and the amount of light reflected or transmitted by that pixel is then measured by the photodetector. The photodetector output is thus a voltage which represents the brightness of the pixel. The range of values over which this voltage can vary is known as the dynamic range of the photodetector's output voltage.
The analog voltage output by the photodetector is then quantized by an analog-to-digital (A/D) converter. The quantization process converts the voltage to a binary number, representing an integer, which is read by the computer. The light source is then focused on another pixel, and this process continues until the entire image is scanned.
The process of converting the analog voltage to an integer invariably involves a compromise. The greater the number of bits available to represent the integer, the greater the range of available unique integers. In turn, this means a better quality quantized image, since the number of available intensity levels will be greater. Similarly, if a color image is quantized, then the image quality will increase as the number of available discrete levels in each of the primary colors increases.
However, as the number of bits used to quantize the intensity of a pixel increases, so too does the cost of the equipment, principally because the amount of computer memory needed to store the image also increases.
As a result, a log amp is quite often used to compress the dynamic range of a video signal such as the photodetector output. The use of a log amp significantly reduces the number of bits required to achieve a particular image quality. For example, when a log amp is used, it is generally agreed that an eight bit A/D converter provides sufficient contrast to approximate the intensity range in a standard television image. Without the log amp, twelve bits are necessary to obtain the same image quality.
A log amp is also used in this application because of the non-linear sensitivity of the human visual system, which varies approximately in inverse proportion to image brightness. A stage of logarithmic amplification, preceding A/D conversion, distributes the discrete intensity levels more efficiently with respect to visual sensitivity and permits a reduction in the number of bits without loss of perceived image quality.
However, introducing a log amp involves another compromise, since any small difference in the log amp's input voltage is transferred to its output, amplified by a factor which depends on the input voltage. This is due to the fact that the gain of a log amp varies as a non-linear, logarithmic function of the input voltage. This problem is particularly noticeable for small input voltages, since the slope of the logarithmic gain curve is particularly steep at the low end of the input voltage range.
Thus, any undesired offset voltage appearing at the input of the log amp, such as that caused by noise, component tolerances, design inaccuracies, drift with temperature or supply voltage, and the like, will have a nonlinear effect on the log amp's output. In fact, any such undesired offset will be magnified if the actual input voltage is low. Careful stabilization of the log amp and very restrictive temperature control are often required to minimize the effect of any such offset voltage.
One prior approach compensates for this effect in a log amp by arranging a potentiometer to null out any offset voltage. See Berlin, Howard, M., Operational Amplifiers, (1979: Heath Company, Benton Harbor, Michigan), pp. 5-11 through 5-14. However, this approach requires a skilled technician to periodically calibrate the potentiometer.
Another technique is to use matched transistor pairs, as in Sheingold, Daniel, ed., Nonlinear Circuits Handbook, (1976: Analog Devices, Inc., Norwood, Massachusetts) pp. 179-188. However, matched transistor pairs are expensive, and even if the expense is justified, semiconductor devices exhibit only limited operational stability over the course of time. This is due at least in part to internally occurring silicon diffusion processes.
The first approach requires repeated human intervention to readjust the potentiometer, while the second approach provides limited temperature compensation. But even when they are used with a quality amplifier, neither is perfect over the long term nor over wide temperature spans. Thus, with either or both of these approaches, null-point instability occurs nonetheless. A lack of null-point stability, particularly in applications where sensitivity is of utmost importance, cannot be tolerated. Because the human eye is quite perceptive to slight variations in brightness levels, particularly at low light levels, image digitization is one such application where the operation of the log amp must be stable. Any instability is even more intolerable in a color image scanner. Such a scanner typically has three photodetector outputs for each pixel, one for each of the red, green, and blue primary colors. Since the three photodetector outputs are eventually recombined to form the digitized image, any offset in one of the channels results in an undesirable hue imbalance.
What is needed is a way to stabilize the output of a log amp so that it is fairly impervious to offset voltages or other drifts in operation over time. This would allow the quantization process to be repeatable from image to image and identical across multiple output channels.
Yet another problem with precision circuit components such as log amps, is due to the fact that the entire system's accuracy depends upon how accurate the log amp is. Some prior systems have thus provided for calibration of the log amp, such as in U.S. Pat. No. 4,335,384 issued June 15, 1982 to Roos. In that system, an exponentially decaying analog signal is used to calibrate the log amp. With this approach, the delay time of the log amp response must be estimated in advance.
In fact, accurate estimation of the log amp's response in advance is quite difficult, especially at the low range of input voltages. Because the bandwidth of the log amp is quite low in this range, and varies as the input voltage increases, the signal propagation delay through the log amp also changes in accordance with the input level.
In many applications it is necessary to characterize the transfer function of a non-linear circuit component accurately in spite of this difficulty. In particular, the response of a "log amp" is only approximately logarithmic and deviates significantly from logarithmic behavior, particularly at the low end of the input voltage range. Furthermore, the transfer function is likely to change over the course of time, as a result of temperature fluctuations, etc. Therefore, a means of calibration may be required, not only for the use of trained technicians during installation or maintenance procedures, but for automatic use during normal system operation. It must, therefore, be relatively fast, accurate, efficient, and reliable. Given this capability, it would then be possible to calculate the input voltage reliably and accurately, by applying the inverse of the measured transfer function to the observed output of the log amp.